Crying "wolf": a response to Wolf

I suppose that given his surname, Daniel understandably felt an urge to
contribute to an exchange on wolves; but I'll assume here that what he
wrote wasn't just a pretext.

Daniel Wolf wrote:
>
> Jonathan Walker has got his history right, but terminology often has a
> life of its own, and now, following my Webster's Collegiate, the
> _wolf_ for tuning is **a dissonance in some chords on organs, pianos,
> or other instruments with fixed tones tuned by unequal temperament**,
> or **an instance of such dissonance** (there is also a definition for
> the faulty tones in certain stringed instruments, and the usual stuff
> about _canus lupus_). I think we should accept the broader definition
> of _wolf_that describes an effect or category of effects, rather than
> specific intervals, and when we intend a specific interval it would be
> best just to give the ratio itself.

I don't want to take the matter any further than this reply to Daniel,
before tedium sets in, but here, for what it's worth, is why I don't
accept his appeal to what might seem, on the face of it, common sense.
Regular dictionaries are not normally adequate for technical terms that
require some theoretical background knowledge, and discussion in any
field beyond the most rudimentary level would be rendered impossible if
some participant were to insist that common dictionary definitions were
the proper basis for the use of technical terms. Even specialist
dictionaries such as Grove can't always be relied upon: anyone wanting
basic information about just intonation from Mark Lindley's entry will
gain a strange and most inadequate conception (the article is almost
entirely about JI keyboards -- try it, if you haven't already).

The second musical definition of wolf, concerning the acoustic
properties of violin etc. bodies, is also well established and quite
distinct -- it ought not to be taken as a sign of how hopelessly vague
"wolf" under another definition has become, any more than it should be
thought to render wolf qua *canis lupus* ambiguous.

The account Webster's gives for the first definition is not only too
vague by my reckoning, but is even misleading; here it is again:

> "a dissonance in some chords on organs, pianos,
> or other instruments with fixed tones tuned by unequal temperament"

This fails badly:
1. Wolves are also formed in non-tempered tunings, both Pythagorean and
just (I suspect the dictionary compiler thought all tunings are
temperaments).
2. Worst of all, wolves are _not_ a feature of the entire range of
well-tempered systems, which are all unequal -- in fact, as I said in
the previous message, well-tempered systems were devised _for the very
purpose of removing the wolf_.

My point, in the previous message, was that the use of "wolf" for a
40/27 collapsed the two problems of a JI 5-limit keyboard into one. The
diminished-sixth problem is shared with keyboards that use a
Pythagorean, meantone or meantone related, or other non-well-tempered
irregular system. The problem of the 40/27 (and other intervals that are
a syntonic comma flat or sharp for the same reason) is unique to 5-limit
keyboards. As a keyboard tuning for late 15th and 16th century music (as
Zarlino intended it), it is of no use; the discovery of the reasons for
this is perhaps the best route towards an appreciation of the virtues of
meantone for keyboard instruments.

In technical discussions, informed participants can only regulate
themselves, collectively; general purpose dictionaries cannot be
expected to serve as final arbiters. If we allow our terminology to
become ambiguous, or hopelessly vague, we have only ourselves to blame.
"Wolf" as in "wolf fifth" or "wolf fourth" is a useful term because it
covers the same phenomenon over a range of different keyboard
tunings/temperaments, and this means, as I said in the previous message
that it covers quite different intervals, e.g. the 3-limit wolf fifth a
Pythagorean comma flat of 3/2, and a 5-limit wolf of 192/125 41 cents
flat, with meantone-related temperaments falling between these extremes.
We even have the prospect of a wolf fifth which is closer to 3/2 than
the regular fifths of one temperament, namely, the 1/10-comma
temperament of the meantone family. The key to the concept, strictly
defined, is to avoid thinking in terms of enharmonic equivalence, and to
think of each note of the upper rank ("black" notes) as fulfilling one
of two functions, but never both; the correct spelling of the interval,
as G# to Eb etc., will always distinguish the wolf interval from the
normal interval in a given tuning, whatever size the wolf interval
happens to be. In the case of the 40/27 problem on a 5-limit keyboard,
the spelling is correctly D to A: this is not a problem of letter names
and sharp/flat chromas, but of plus/minus syntonic comma inflections.

Fragmenting this phenomenon by stating precisely (by ratio) which
intervals are concerned -- as Daniel suggests -- falls short of a
complete solution: there are theoretical and historical contexts (in
15th to 18th century music) where a given piece could and would have
been rendered according to different tunings, and "wolf" is needed in
such contexts. Quite apart from being inappropriately precise in these
contexts, how many people could tell, at a glance, what 192/125,
262144/177147 and 128/5^(11/4) all have in common?

(Answer: The wolf fifths of the just, Pythagorean and 1/4-comma meantone
systems respectively, which lie 41 cents sharp, 23.5 cents flat and 35
cents sharp of 3/2, but are each the diminished sixth within their
respective systems.)
--
Jonathan Walker
Queen's University Belfast
mailto:kollos@cavehill.dnet.co.uk
http://www.music.qub.ac.uk/~walker/

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